Abstract
In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of superdiffusions X corresponding to the evolution equation ∂ t u t =Lu t +βu t -ψ(u t ) on a domain of finite Lebesgue measure in R d, where L is the generator of the underlying diffusion and the branching mechanism ψ(x,λ)= 1/2α(x) λ2+∫0∞(e-λr- 1+λr)n(x, dr) satisfies supx∈D∫0 ∞ (r r2) n(x, dr)<∞.
Original language | English (US) |
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Pages (from-to) | 73-97 |
Number of pages | 25 |
Journal | Acta Applicandae Mathematicae |
Volume | 123 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2013 |
Keywords
- Martingale
- Point process
- Principal eigenvalue
- Strong law of large numbers
- Superdiffusion
ASJC Scopus subject areas
- Applied Mathematics